Two particles travel along a straight line. Both start with the same time are accelerated
uniformly at different rates. The motion is such that when a particle attains the maximum
velocity 3V, its motion is retarded uniformly. The two particles come to rest simultaneously
at a distance X from the starting point. If the acceleration of first is 2A and that of second is
A, find the distance between the points where the two particles attain their maximum
velocities.
Answers
X/3 is the distance between the points where the two particles attain their maximum velocities.
Explanation:
Initial Velocity = 0
Final Velocity = 3V
Acceleration = A & 2A
Apply the formula
V² - U² = 2aS
=> S = (V² - U²)/2a
S =( (3V)² - 0²)/2A & ( (3V)² - 0²)/A
S = 9V²/2A & 9V²/A
Distance in between = 9V²/A - 9V²/2A
= 9V²/2A
as Initial , Peak & final Velocity is Same with uniform motion
& total Time taken Distance is same hence their acceleration will just get interchanged
Hence Total Distance = 9V²/2A + 9V²/A = X
=> 27V²/2A = X
=> 9V²/2A = X/3
Distance in between where the two particles attain their maximum velocities.= X/3
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